CHS AP Calculus

Free Advice from 2006-2007 Students

2007-08-17T08:28:00.000-05:00

Free advice from last year's class:

Do your portfolio each chapter before the chapter exam; it will really help you to understand the info better. Plus you will have a lot less stress when it comes time to turn in your portfolio. Do the homework. Know your parent functions and what they look like. Know the unit circle by heart. Know how to do the problems with yams in them because you will see very similar ones on the tests. Have a good attitude, it will definitely be a difficult cours but you will neet to be positive in order to be successful.

Learn the material before the test. Don't use the tests as a way to figure out problems for the first time. Time is of the essence in this class. Know your stuff and use the tests to show it off. Ask the questions you need to ask to make sure you get it. Don't worry about sounding too dumb or too smart. From questions comes learning. As you will hear Mr. May say, "Make it your own."

Read the section in the book the night before. It truly does help. Review stuff you don't know very well every night. When you get tests back correct you mistakes while going over it. Then review your tests for future tests. Calculus is difficult but not impossible. Survive until second semester! Don't give up. Don't wait until the night before it is due to do your portfolio.

READ. Life is so much easier when you read and get it all down the first time around. Take notes. Going back and looking at the examples he gives you could be the difference between understanding the material and remaining lost. Don't wait until the night before the portfolio is due to do them. You won't have time!!

Do your homework every day you get it.

Ask questions out loud during class. If you are in a team, use your team. If you do not like math take another class.

Relax! You learn better if you just calm down. No noe will get their head chopped off. You need to do the homework. It is a must to be successful. If you don't get something, ask questions. You'll find that being shy is a bad thing.

KNOW THE UNIT CIRCLE!!! Portfolios ar meant to help you out -- it is worth the effort come the end of April. It really isn't as bad as people make it out to be.

When you are doing your homework, if there's a problem you don't understand, take the time to work it out. Try to go to sleep early in order to wake up early and get extra help from Mr. Mayo on anything you couldn't figure out. Work on the portfolio ahead of time. It is doable the night before, but then you probably won't get a chance to sleep at all that night. Good luck!

Always do your Calculus homework first. It is much easier to concentrate at 4:00 than it is at 10:00. If you do not understand a problem, go in for help in the morning. Mr. Mayo will not eat you, I promise. Know the unit circle - seriously. Do not get behind on your portfolio. It is way too much to do the night before. Keep everything: notes, tests, hand outs, worksheets, etc. You will want them come AP time. When you are in groups, talk to each other! It is much easier to learn that way. Making flash cards for equations/Taylor Series/whatever really helps. Read the chapter the night before the test. The true/false questions at the end are quite useful.

If you have never had to study for a previous math course, don't think it will be the same for Calculus. Even if you understand everything in the chapter, don't take it as "I don't need to study. I got this." You will get burned if you don't take just a little bit of time to review. And don't cram the night before or the day of the test -- start reviewing at least a coupld of days before. Do the Calc portfolio as you go along. It took me a couple of all-nighters before I finally learned this valuable information. Never say, "I don't know," which means do your homework. Read the section the night before. Bad grades on those little 6-poing quizzes will be hard to make up as the end of the 6-weeks approaches.

Free Advice from 2005-2006 Students

2006-08-24T07:12:00.000-05:00

Once again this year after the AP Exam, I asked the students what advice they would give to those following behind them. Here you have it.....

Get in the habit of staying current on the lesson and the homework. You will quickly find that falling behind is not an option.
If you're not sure you are understanding something, say so. Chances are someone else is thinking the same thing you are.
You will not remember a process simply by seeing it done for you. Get in the habit of taking your own notes with all examples that are done for you.
Just as Mr. Mayo suggests, compile a "cheat sheet" that contains easily forgotten formulas, rules, and theorems.
Regardless of what you may think coming into this course, the grade you receive will accurately reflect how much effort you put forth, so consider the first before you shortcut on the second.

Understand concepts, general ideas.
Only be concerned with memorization secondly.
Never be close-minded when approaching problems, there may not be a single method of obtaining the solution.
Never feel inferior because you are incorrect.
Try as much as possible.
If you cannot understand something, sit and look at it and try to wrap your mind around it.
Visualize everything.

Respect the Calculus! It is a gift that should be used and cherished.
Do your homework! You might think that you are pulling a fast one because Mr. Mayo is not grading it, but it will catch up with you.
Study! If you think that you know the chapter like the back of your hand, there will be the one question on the test that you forgot about but could have studied.
If Mr. Mayo says that you should study something, study it! He is not out to trick you. If he says it is on the test, then it is on the test.
If you do not understand something, go in for help! Mr. Mayo loves helping people if they need it and he might even drop a very helpful hint.
Just learn for learning's sake. Don't worry if it will be on the test or not. Just learn it because it's good to know. By the way, it will be on the test.
Don't worry about your grade! If you just worry about learning calculus then your grade will take care of itself. Also, worrying about your grade makes a certain someone a little angry.
Have fun! That one doesn't really need an explanation.

Do the homework: you will be glad you did later on.
If you don't understand something, ask about it. It's better to look stupid before you supposed to know it than to look stupid when you get a really bad grade back.
Don't procrastinate on the portfolio.
If you procrastinate on the portfolio, set more than two alarms the morning it is due.
Use the portfolio as a study guide for midterms and the AP Exam.
Make sure your calculator is on RADIANS!
Learn the unit circle!!
Know that a stilleto is not always a shoe.

Do all of your homework every night.
If you don't understand something go in for extra help.
Realize that it is the class vs. the AP Exam, so work as a team with everyone in the class.
Do all of your homework every night.
Help each other out.
The day before a test, get together in a small study group and go over questions and free responses relating to that section.
Don't wait for the last minute to do your portfolio, keep up on it.
Have confidence in your ability to learn and understand calculus.
Don't get frustrated because you can still get a 5 on the exam even though you missed some questions.

Take Calculus as a Senior.
Work on your portfolio every night.
Come in for help.
Ask questions!!!
Call your peers.
Study for tests individually and in groups.
Do ALL of your homework (at home!)
Don't miss class.
Don't give up.
Always work hard.
Never sit on the desks.
Don't beat yourself up, stay positive.
Make sure you have the time for Calc.
It's not for everyone.
Don't take it to raise your GPA.
Don't argue with him about grades (you want your partial credit, believe me!)

Do your calc homework FIRST - you will always have it so it can become routine.
Read the next section, or two.
Take good notes - it really helps.
Pay attention in class and ask questions - you are usually not the only one who is confused.
Use the internet to study and understand - calculus can be taught in many ways, maybe another one is better for you.
Use your colleagues, talking to others ALWAYS helps.
Come in early, stay after, stay up -- care.
Study a little each night.
I'm not going to say do your homework, if you don't you're stupid. Period.

Assignment: Technology

2005-12-07T13:31:00.000-05:00

In the book Good to Great, Jim Collins and his team of researchers identified a set of elite companies that made the leap to great results and sustained those results for at least fifteen years. The research team contrasted the good-to-great companies with a carefully selected set of comparison companies that failed to make the leap from good to great in order to determine why one set became truly great performers while the other set remained only good.

One area that the researchers considered was the use of technology by the companies. Collins’ team found that, “when used right, technology becomes an accelerator of momentum, not a creator of it. The good-to-great companies never began their transitions with pioneering technology, for the simple reason that you cannot make good use of technology until you know which technologies are relevant.”

You have used technology in your study of the Calculus this semester. In this assignment, I want you to discuss the role of technology as you see it in the study of mathematics in general and Calculus in particular. Has it been an accelerator of learning or a hindrance? Has it assisted you or not helped. Support your answers with concrete examples. Please write this entry in the form of an essay prior to entering it on the blog.

Assignment: PDSA Part 2

2005-11-20T08:25:00.000-05:00

Now that we have completed the second six-week term, I want you to again reflect on your experience in AP Calculus. Think about all the topics and concepts that we have explored. What seemed the hardest? Why? What was the easiest? Why?

Assignment: Favorite Functions Revisited

2005-10-20T12:42:00.000-05:00

Now that we have explored the derivatives of functions, it is time to take another look at favorite functions. This time I want you to choose a function whose derivative function you like and explain why you chose it.

Mine is good old e to the x. You probably know why. Sure, it is its own derivative. Imagine that. A function whose rate of change is the same as the function itself. What a concept!

Assignment: Plan, Do, Study, Act

2005-10-06T20:29:00.000-05:00

At the end of WWII, General Douglas McArthur was placed in charge of the army of occupation in Japan and was tasked with rebuilding the country. He called upon the assistance of Dr. W. Edwards Deming, a statistician whose methods had been shunned by American industry. As it turns out he was instrumental in getting Japan's industrial base back on its feet. In less than 50 years, Japan went from making cheap and low added value products to the manufacturing of the highest quality precision work in the world and we probably know the rest of the story as we look around to see Honda, Sony, Mitsubishi, et. al.

Deming is credited with developing a tool called the Deming Cycle also known as the PDSA Cycle. The cycle is a tool for continuous improvement. PDSA stands for Plan-Do-Study-Act. Deming maintained that as we go through life with all of its processes, we should strive for continuous improvement by applying the cycle.

Plan: Plan ahead for what we are going to do.
Do: Execute our plan.
Study: Study the results of our plan.
Act: Decide if we are happy with the results and then make changes as necessary.

The cycle is never-ending and should result in continuous improvement. As I have coached over the years I have urged my runners to analyze their performance by determining what they were happy with, what they were unhappy with and deciding how to change. As the first 6-week term ends, it is time for you to do just that. Please take some time to reflect back upon your experience in AP Calculus for the first term. What are you happy with? What do you want to change? How are you (we) going to change it?

Assignment: Real Life Derivatives

2005-09-29T10:19:00.001-05:00

Now that we have explored the meaning of the derivative of a function, let's think about some things in our worlds that can be modeled using rates of change. My example is my 1969 Volkswagen Westfalia. It is obviously old and, because I live at the beach, it has to endure the harsh elements. So, what does this have to do with functions, you ask. Well, I am constantly worrying about rust. My function is the amount of rust on my VW as a function of time, R(t). As much as I wish it were not the case, I think this is probably an increasing function. The more rust there is, the more there is going to be. Perhaps a never ending battle with the elements. Oh to own a garage.

What is the meaning of the derivative of my rust function? Liebniz would consider dR/dt...the change in the amount of rust with respect to time. In other words, the amount of rust that is added at any given moment. Argh, continuous function? Does that mean my beloved Math-Mobile is rusting away as I write this? Maybe I should get out of here and start sanding and grinding. Ah but back to the Calculus...

In this blog, I want you to consider some function in your world and discuss the meaning of the derivative of your function.

Assignment: Mastery

2005-09-11T20:58:00.000-05:00

As we have discussed in class, our goal this year is to master the Calculus. What does this mean? When thinking of mastery, several things come to mind. One is the London Taxi Drivers' Test. Can you imagine having to take a rider anywhere in London, a city designed and built long before the advent of the automobile, based entirely on being given an address?

Another example comes from the recently released DVD of the poet laureate of the great state of New Jersey, Bruce Springsteen as he describes writing the lyrics to "The Rising." Mr. Springsteen says, "These are the songs that you wait for. Did I think of any of this prior to writing the song? Nope. But I felt all of it when I was writing the song. Over thirty years you internalize your craft and the mechanics of story telling; it becomes like a second language. You speak without thinking. It's like a second skin that you feel with. So you pray to the gods of creativity and aliveness that you remain awake and alert and in command of your senses so that when the moments arrive you are ready."

Finally, one of my favorites comes from the opening scene of the movie "Caddyshack" in which Chevy Chase plays Ty Webb:
Ty: "I like you Benny."
Danny: "That's Danny, sir."
Ty: "Danny...Let me give you a little advice. There's a force in the universe that makes things happen and all you have to do is get in touch with it. Stop thinking, let things happen, and be the ball. (Covers eyes with blindfold.) Danny, where's the wedge?"
Danny: "It's right here, sir."
Ty: "Thank you Danny. Find your center, hear nothing, feel nothing." (Hits ball over water trap and it lands within 2 feet of the hole.)
Danny: "That was incredible, sir"
Ty: "You try it. Just relax, find your center, picture the shot, Danny. Picture it. Turn off all the sound. Just let it happen. Be the ball, Danny. You're not being the ball, Danny."
Danny: "Well, it's kind of difficult with you talking like that."
Ty: "OK. I'm not talking. I've stopped talking. I'm not talking now. Be the ball. (Danny hits ball and it lands in the water.)
Danny: "Where'd it go?"
Ty: "Right in the lumber yard."

So as we embark upon our journey to attempt to master the Calculus, I want you to reflect on things in your life that you have already truly mastered. What do you do in your life where you act without thinking, where you are the ball, what is your second skin?

Assignment: "The Special Instrument"

2005-08-29T15:46:00.000-05:00

"As it campfires glow against the dark, every culture tells stories to itself about how the gods lit up the morning sky and set the wheel of being into motion. The great scientific culture of the West, our culture, is no exception. The calculus is the story this world told itself as it became the modern world.
"It is the calculus that for the first time allowed mathematicians access to the Book, and in Newton's hands it is the calculus that became his special instrument... and ours.
"However much Newton may have passionately pursued pure mathematics, he was not in his heart purely a mathematician; during the year of miracles, it was something else that seized his imagination, some supected barely felt connection between the mathematical garden in which he had wandered with such careless authority and the massive collocation of astronomical and terrestial facts that were his to touch and tame as well. Like Einstein, his spiritual heir and only equal, Newton viewed mathematics as an instrument. In thinking about the calculus, Newton was already thinking beyond the calculus, planets in motion and falling objects moving across the enormous corridors of his mind. Let them move and tumble, those pale planets and falling objects. Something is forming itself.
"Time and space make up the the world's great vault. It is within that vault that change occurs. The night sky is lit by moonlight, the great trees sway, birds shriek, and then the opalescent light vanishes and the sun appears. Something has changed because some things have changed. This is the familiar, the continuous world. and it is this world that Newton represented by a series of daring correlations."

-- David Berlinski from Newton's Gift and A Tour of the Calculus.

Assignment: After reading "The Special Instrument" handout, list some things that are important in your life that are continuous. What would your world be like if we could not explain these things?

Functions

2005-08-25T19:07:00.000-05:00

"Mathematics is conceived in the fires of the real world, and the functions that bring twitching life to the calculus represent processess beyond the closed coffin of a coordinate system -- things that take place in time and that take place in space. The maturation of an egg and the education of an undergraduate both represent processess; so does the circumnavigation of the moon, the beating of the human heart, and the dense shifting of the seas under the influence of the lunar tides. But not every functional relationship, it is important to recall, is a relationship between numbers. There is a world of relationships beyond the world of mathematics in which men and women pair off, children are raised, scores are settled, and fathers age and then die, and none of this correlated with the real numbers. And not every relationship between numbers expresses an interesting mathematical function. Surrounded somewhere in Las Vegas by blue-haired women and hard-eyed men, a roulette wheel spins in the soulless night. It generates a string of random numbers. The association between those numbers and the time at which they are generated describes a matching of numbers to numbers and so a function. It is an association without structure and so without interest. The functions of the calculus represent, they embody, the mathematician's canonical instruments for the depiction of change. They have up to now appeared as a collection. Mathematics is, in part, a rhapsodic subject, full of dark mystery; but it is also a discipline like comparative anatomy in which things are put in their mathematical places and places found for mathematical things." David Berlinski, A Tour of the Calculus

Assignment: Favorite Functions

2005-08-23T19:39:00.000-05:00

What is your favorite function?

Mine is good ol' f(x) = x squared. He is my favorite for many reasons. First he is always in a good mood and is never negative. Secondly, he is even-tempered -- f(-x) always equals f(x). I also like him because no matter what x-value I choose, f(x)'s rate of change is always constant and ends up being twice the x value. Finally, I think he is cool because whether his x-values go toward positive or negative infinity, his graph climbs toward the sky.

Name your favorite function and explain why you chose him/her.

Free Advice from 2004-2005

2005-08-23T16:32:00.000-05:00

The day after the AP Exam this year while we were sitting around enjoying our donuts, I asked the class to write down any and all advice they wanted to give the incoming class on how to succeed in AP Calc. Listed below are their comments.......Food for thought as you embark upon your Calculus careers......

1. Expect to work hard.
2. Don't procrastinate on the Calculus Portfolio or life will s___ really bad.
3. Do your homework!
4. Don't be afraid to ask questions and go in for extra help outside of class.
5. Don't be shy....or you die! -- MM.

Don't wait until the night before your Calculus portfolio is due to do it.
It always takes much longer to type it than you expect...every time.
If you finish MM's sentences on funny comments/philosophies he sometimes gives extra points.
Do the homework every night!
Ask MM for help outside of class time.
Get a study buddy or people you know you can call to ask questions about homework. Math really is easier as a "Team Sport."
Know your unit circle.
Even when you get really really frustrated, just try to remember that eventually you will get it.
Know your Saturday Night Live, Monty Python, and Caddyshack ("Be the ball.").
MM loves jelly bellies.
Cover your book.

Do your HW every night. It helps.
The Calculus portfolio takes longer to type than you think.
If you are going for multiple AP classes, prepare to have minimal social life.
Laziness is extremely dangerous.
Finish his sayings out loud.
Ask for help outside of class.
Make sure there is at least one other Math god or goddess in each of your classes so you have someone to share inside jokes with.
Watch a lot of SNL, Monty Python, Best of Will Ferrell and Caddyshack so you understand.

Don't ever wait until the night before your portfolio is due. It takes longer to type than you think.
Don't wait until the night before to study for a test. Study a few nights out, so you can hit your weak points the night before.
Speak up in class. He likes to see that you are at least trying, even if you are wrong.
Don't be afraid to speak up if you think others are wrong and you have justification as to why. Everyone makes mistakes.
Always do your homework. The practice helps a lot and you can identify mistake you made.
When MM says, "You'll need to remember this," you will! Write it down.
If you are confused, don't be embarassed, ask because at least 1 more person is as confused as you are (usually).

Don't play basketball at the Calculus Lock-In, you might break your foot!!!
Don't focus on grades. When all is said and done it is more fulfilling to know that you truly understand the Calculus than it is to have an A. Also when it comes time for the (AP) Exam your grade in the class won't help you.
Don't avoid learning things that you have trouble with. They will never go away and they will only add stress to your life.
Pay attention during class. If you miss a single step because of daydreaming you won't understand anything that follows.
Don't ever say you hate math, at least not in front of MM. Never challenge his ability to win the Iron Man competition.

Do not be afraid to ask for help.
Be ready to study for hours for tests.
Calculus portfolio - don't wait until the last night unless you simply hate sleeping.
Watch out for yams, ferrets, and sheds.
Be the ball; you need more cow bell; scoff at the shed.

Do your hw.
Expect to work hard.
Learn the concepts.
Remember the formula for area of a triangle.
Enjoy the journey!
Stay focused!

- Start studying before the night before a test.
- Don't blow off the midterms; especially the last one of 1st semester. It can make or break your semester grade.
- Don't let senioritis set in until after the AP Exam.

As a pain as it may be, do your portfolio gradually, not the night before it is due. When MM keeps emphasizing something in class, chance are it will be on the test. Look at the questions at the end of the chapters. If it inolves a yam, it will be on the test. Finish his quirky sayings and you get extra points. Do your homework -- just do it. Or you will fail horribly. Don't pull all nighters more than twice a week -- you will crash and burn. Make sure your first period is a BS class so you can study. Design the Calculus t-shirt before the last minute. Watch SpaceBalls, Paper Chase, Will Ferrell Live, Field of Dreams, Caddyshack and the scene from Saturday Night Live with the cow bell so you won't be truly lost with his inside jokes. Mutter cuss words under your breath in order to confuse your fellow classmates. Don't leave bits of trash on the floor. If you're lost, grow some ____ and raise your hand and ask what on earth is going on. Stay in Calculus because you get donuts.

Do your homework
Eat your yams,
Don't let senioritis
Kick in till after exams.

Don't be ______
Pay attention take notes,
If you check the van
Be sure to bring coats.

Take the advice
Of Godfather M___
Bring a cowbell
And you'll all sing "Dao"

The beginning is tough,
So don't turn red.
And if you study the right thing
You'll scoff at this shed.

Do your homework
Don't be too cocky.
You're responsible for your own grade. There isn't any coddling.
Be motivated.
Learn to study.